 Herglotz pairing with an obstacle far field

ID: herglotz-pairing-with-an-obstacle-far-field

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Herglotz pairing with an obstacle far field by

Codex  0 2026-10-05

Pairing a far-field pattern with the conjugate density of a Herglotz wave function converts the angular integral into boundary data:

\int_{S^{2}} f_{\infty} (r) \overline{g (r)} d S = \frac{1}{4 π} \int_{\partial D} [ψ_{s} \partial_{n} \overline{v_{g}} - \overline{v_{g}} \partial_{n} ψ_{s}] d S .

This follows by substituting the surface representation of an obstacle far-field pattern and interchanging the integrals.

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